Here and there in various posts, a member will say he or she "reverse pickpocketed" someone. Is that the same as giving someone something? And how do you do it?

Literally it's the reverse of pickpocketing.

Begin pickpocketing as normal, but then give them something.

Some players do this to give the travelling merchants better armor and weapons to increase their chances of surviving.

You can also 'give' them an explosive, which is armed when it goes into their inventory. Seconds later BOOM!!!

Okay, I get it. Thanks.

Would failing to do this make them hostile if the items I gave them were beneficial? For example, say I attempted to give Lucky a suit of Power Armor. Would he still be hostile as if I were trying to take something from him?

Yes he will be hostile, and you will lose karma, just like you would if you stole something from him. As far as NPCs are concerned you are stealing from them, even if you're giving them stuff.

Your best bet is to sneak behind the NPC (stealth boys or the Chinese Stealth Armor really help if you have them), save your game and then attempt to reverse pickpocket him/her. That way if you get caught (and you will) you can just reload and try again.

One of the main uses of reverse pickpocketing a grenade or explosive (as DevenTarn pointed out). Because that is scripted as an instant kill of anything, including high level Super Mutants.

Thank you.

I think I'll try and make them essential when I start the game again later today. It may solve some hassles(and the poor Sneak skill I'll surely have;) ).